SCALABILITY CONCERNS OF CHIRP SPREAD SPECTRUM FOR LPWAN APPLICATIONS

International Journal of Ad hoc, Sensor & Ubiquitous Computing (IJASUC) Vol.10, No.1, February 2019
DOI : 10.5121/ijasuc.2019.10101 1
SCALABILITY CONCERNS OF CHIRP SPREAD
SPECTRUM FOR LPWAN APPLICATIONS
Aiju Thomas1
and N V Eldhose2
1
School of Technology and Applied Science, M G University, Kottayam, India
2
M G University, Kottayam, India
ABSTRACT
Divergent modulation schemes have been proposed for the Internet of Things (IoT). Low Power Wide Area
Networks (LPWAN) technologies are gaining unprecedented acceptance in IoT application of sensor
networks. Chirp Spread Spectrum (CSS) is a prominent modulation technique proposed for LPWAN. Chirps
can traverse long distance and are resilient to noise and Doppler effects. Noise resilience along with
transmission range and low power requirement makes CSS a preferred modulation scheme for sensor
networks. LoRaWANTM
, with its physical (PHY) layer using CSS, has emerged as the widely accepted
LPWAN solution. By using CSS modulation with orthogonal spreading factors (SF), LoRa offers wide
coverage to LPWAN applications while supporting a high volume of devices. However, scalability
performance of CSS has not been inadequately modeled. As with the suitability of the modulation scheme,
there are concerns on how chirps interact with the surrounding as the number of deployments bursts out
into higher volumes. We evaluate CSS at ISM band 868 MHz for spreading factor 7 to 12 at bandwidth 125
kHz for performance and scalability. Simultaneous transmissions were simulated with repeated iterations
and conclusions are arrived on collisions rate, packet error rate, and bit error. Suitability of using CSS for
sensor networks for future deployments is commended.
KEYWORDS
LoRA, LPWAN, Sensor networks, CSS, Chirp Spread Spectrum, Packet error, collision
1.INTRODUCTION
Internet of Things (IoT) is a paradigm that creates a panoply of interconnected devices.
Widespread deployment of IoT imposes complexity in communication and heterogeneity among
devices which communicate over the Internet. The current deployments of things are in the order
of 50 billion and by 2020 and will encompass 1000 times more connected devices, all with
different requirements. There are concerns about how devices will interact with the surrounding
and among themselves. This is however difficult to assume as today’s network is limited with its
ability to address the requirements of future deployments. The scalability of networks is a concern
as to cope with the ever-growing number of devices [1]. Machine to Machine (M2M)
communication as part of IoT is characterized by divergent modulation schemes. Modulation
schemes are application specific, depends on the volume of data handled and range. A
surveillance camera is required to deliver a huge volume of data, whereas applications like
metering handle a small amount of data while being stationary. IoT applications such as sensor
networks are often battery powered and require scalable low power wireless technologies. Low
Power Wide Area Networks (LPWAN) has been proposed to address the needs of long-range and
low-power IoT applications in the field of sensor networks.
Wireless sensor networks currently practice cellular-based technologies or multi-hop short-range
technologies for LPWAN [2]. Devices or things use dedicated protocol stack to cope with the

2
constraints of an end device. Constraints are set on power usage, range, computing capability, and
bandwidth. In these networks, one of the things needs to connect to the internet through an
internet protocol (IP) forming gateway whereas all the other form network among them in star or
mesh topology. Applications and services are deployed at the top of the protocol stack which
either runs locally or as part of the cloud.
There are standards that operate mostly at 2.4 GHz and optionally in the 868/915 MHz,
unlicensed frequency bands used to connect things. Prominent among them are
• Near Field Communications (NFC) for short range applications;
• Radio Frequency Identification (RFID) systems for active or passive networks;
• ZigBeeTM
, 6LoWPAN, Thread-based systems under IEEE 802.15.4 standards;
• BluetoothTM
, Bluetooth Low Energy (BLE)TM
;
• IEEE 802.11 based Wi-FiTM
;
Majority of these protocol use IEEE 802.15.4 based standard. These standards are weak in
penetration capability and suffer heavy bandwidth interference. These technologies cannot be
deployed for sensor networks due to range limitations. Another popular alternative is cellular
networks connecting devices to the IoT gateway. The devices running on cellular networks use
power-hungry algorithms for signal decoding. Deployments of such networks are expensive and
the difficulty in device certification limits their application for sensor networks. Cellular networks
are minimal in success addressing to LPWAN space despite its formidable presence. 2G cellular
technologies are fading out: there are 30 million 2G base stations in the US alone which are to be
orphaned [3]. 4G LTE or 5G with much more spectral efficiency is about to replace 2G
technologies, leaving the carriers with no choice accepting consumer demand for high data speed.
4G and 5G networks cannot ensure scalability considering the volume of future deployment.
LPWAN which utilize the sub-GHz band and are can provide several kilometres of outdoor
coverage. There have been efforts to reduce the bandwidth requirement for IoT devices. Driver
encapsulation [4] techniques reduce bandwidth requirement hence enhance spectral efficiency of
devices. The paper is organized in three sessions. Technologies related to LPWAN are discussed
in session 2. Session 3 covers mathematical representation of CSS to aid simulation. Session 4
covers simulation environment and results.
2. RELATED TECHNOLOGIES
In order to help the reader better understand LPWAN, three prominent technologies supporting
LPWAN for sensor networks are presented in this session.
2.1. SIGFOXTM
Sigfox was proposed for the IoT market in 2009. They have a distinct market share since then.
Sigfox operates in the 200 kHz using the ultra narrow band modulation [3]. Each message is 100
Hz wide and transferring at 100 or 600 bits per second, depending on the region. Sigfox can
achieve long range while being robust against noise. An uplink message has up to 12 bytes
payload and takes an average 2s over the air to reach the base stations which monitors the
spectrum for Ultra Narrow Band (UNB) signals. For 12-byte data payload, a Sigfox frame uses 26
bytes in total [5]. The payload allowance in downlink messages is 8 bytes. A device is not
attached to any specific base station like cellular networks. The broadcast messages are received
by an average of three base stations in the range, and necessary approximations are made to

3
decode the correct data. The first released technology supported only unidirectional uplink,
however, bidirectional communication is now available [3]. Sigfox claims that each gateway can
handle up to a million of connected objects, with a coverage area of 30–50 km in rural and 3–10
km in urban. But deployment to test the claim in terms of scalability is not achieved so far.
Evaluation of network scalability cannot be performed as the technical details are kept
unpublished as the protocol is proprietary in nature.
2.2. INGENUTM
Ingenu is a preparatory LPWAN which has been around for Machine to Machine (M2M),
Wireless Sensor Networking (WSN) and IoT [6]. Random Phase Multiple Access (RPMATM)
uniquely addresses hundreds of IoT devices. RPMA was designed to provide secure LPWAN
solutions at 2.4 GHz band pioneering the 802.15.4k [7] standard. Despite the operating band at
2.4 GHz, the robustness of physical layer design can provide over long-range propagation under
the most challenging RF environments.
2.3. LORATM
LoRa is a proprietary spread spectrum modulation scheme which is a derivative of CSS. LoRa
trades data rate for sensitivity within a fixed channel bandwidth [8]. It implements a variable data
rate, utilizing orthogonal spreading factors, which allows the system designer to trade data rate for
range or power and optimize network performance at a constant bandwidth. LoRa uses wideband
linear frequency modulated pulses [9] whose frequency increases or decreases over a certain
amount of time to encode information. This method will substantially increase receiver
sensitivity due to the processing gain of the spread spectrum technique and exhibits a high
tolerance to frequency misalignment between receiver and transmitter.
3. CHIRP SPREAD SPECTRUM
Chirps are linear frequency modulated wideband pulses that are characterized by low power
consumption, resilience to fading and Doppler effects. CSS combined with digital modulation
schemes such as Binary Orthogonal Keying (BOK), Quadrature Phase Shift Keying (QPSK) and
Differential Phase Shift Keying (DQPSK) can deliver better performance in Bit Error Rate (BER)
[10]. Chirp Spread Spectrum (CSS) was initially proposed by Winkler for communication [11]
and was applied to digital communication by Berni [12]. CSS is now being adopted for sensor
networks due to its low power requirement, resilience to channel degradation by multipath fading
and Doppler effects. IEEE 802.15.4 adopts CSS for Low Rate Wireless Personal Area Networks
(LR – WPAN) for range and mobility. IEEE 802.15.4a standard [13] speciﬁes CSS in two
optional physical layers to support extended range.
• Ultra Wide Band (UWB) model, spanning from 2 to 10 GHz frequency.
• UWB model for the frequency range from 100-1000 MHz
Narrowband frequency located within the mentioned range can be derived by a simple bandpass
ﬁltering. IEEE 802.11ah [14] is an extended range wireless protocol standard in sub-Gigahertz
ISM band (863–868 MHz in Europe, 755–787 MHz in China and 902–928 MHz in North
America) which minimize contention by extending their reach with low transmitted power. Radio
propagation at these frequencies allows signals to travel greater distances, opens up opportunities
to use with IoT. Semtech’s LoRa™ [9] provides low power, low-cost long-range communication

4
for IoT applications. LoRa™ utilize chirp spread spectrum for long-range communication. In
LoRaWAN™ transceivers communicate with LoRa™ gateway which connects to the internet.
This paper examines LPWAN sensor networks in terms of Bit Error Ratio (BER), the number of
packet collisions and packet error rate using MATLAB™. Evaluation is perfumed considering
CSS as used LoRa physical layer. Modulated chirp signals were transmitted through an Additive
White Gaussian Noise (AWGN) channel and evaluated for performance by varying Signal to
Noise Ratios (SNR). Decoded signals are iterated manifold for consistency in results. A detailed
mathematical model for CSS is presented in forthcoming sessions. Packet error rate and the
number of collisions were analyzed with considerable numbers of sensors communicating
simultaneously. Conclusions are drawn on scalability and range of CSS in LPWAN sensor
networks.
3.1. MATHEMATICAL REPRESENTATION OF CHIRPS
3.1.1. LINEAR CHIRPS
Constant amplitude linear chirps are denoted as [6] [15] [9]
𝑥(𝑡) = 𝐴 cos(𝜃(𝑡)) (1)
where: θ(t) is the phase for a given time t
A is the amplitude of the chirp which is constant for a given chirp duration T sec outside
which, A is zero.
Instantaneous frequency of the chirp can be represented as
𝜔(𝑡) =
𝑑
𝑑𝑡
(𝜃(𝑡))
(2)
Time linearity of chirp can be achieved by making phase quadratic
𝜃(𝑡) = 2𝜋µ𝑟𝑡2
+ 2πf0t + ϕ (3)
Instantaneous angular frequency which is the derivative of phase θ(t) becomes
𝜔𝑖(𝑡) =
𝑑
𝑑𝑡
𝜃(𝑡) = 4𝜋µ𝑡 + 2𝜋𝑓0
(4)
Instantaneous frequency in Hz is given as
𝑓𝑖 = 2µ𝑡 + 𝑓0 (5)
In equation (5) frequency varies linearly with time with starting frequency at 𝑓0 . The rate of
frequency change for chirp duration T secs is given as
𝑘 = 2µ𝑡 =
(𝑓1 − 𝑓0)
𝑇
(6)

5
Sinusoidal sweeping frequency from 𝑓0 to 𝑓1 with phase as derivative 2𝜋(𝑘𝑡 + 𝑓0) is given as
cos(2𝜋
𝑘
2
𝑡2
+ 2𝜋𝑓0𝑡)
Linear chirp is represented in terms of time varying instantaneous frequency
𝑥(𝑡) = 𝐴 cos(2𝜋𝑓(𝑡)𝑡 + 𝜙(𝑡)) (7)
where
𝑓(𝑡) =
𝑘
2
𝑡 + 𝑓0
In equation (2) if 𝜃(𝑡) is constant then frequency is zero, if 𝜃(𝑡) is linear then frequency is
constant and if 𝜃(𝑡) is quadratic then frequency is linear.
3.1.2. Chirp Spread Spectrum as used in LoRa
LoRa utilizes CSS in its physical layer symbol modulation. Symbols are chirped using linear
chirps. Chirps are spread to the entire spectrum of the carrier. CSS maintains constant
timing and frequency offsets, reducing the complexity of receiver [9].
Spectral spreading is achieved by varying 𝜙(𝑡) of the chirp signal. Specific time function of
raw chirp 𝑓(𝑡) exhibits linearity as
• Increases from
−𝑏𝑤
2
to
𝑏𝑤
2
for up chirps.
• Decreases from
𝑏𝑤
2
to
−𝑏𝑤
2
for down chirps.
Where: 𝑏𝑤 is the spectral bandwidth in Hz.
Figure 1. Chirp modulation of nth
symbol

6
𝑓(𝑡) in terms of chirp duration 𝑇𝑠 and 𝑏𝑤 is given as
𝑓(𝑡) = ±
𝑏𝑤
𝑇𝑠
𝑡
(8)
Bandwidth and symbol period are related as
𝑇𝑠 =
2𝑆𝐹
𝑏𝑤
𝑠𝑒𝑐𝑠
(9)
Where 𝑆𝐹 the spreading factor ∈ [7,8,9,10,11,12]
Symbol rate 𝑅𝑠 is given as
𝑅𝑠 =
𝑏𝑤
2𝑆𝐹
=
1
𝑇𝑠
(10)
Data rate 𝑅𝑏 is derived as
𝑅𝑏 = 𝑆𝐹
1
2𝑆𝐹
𝑏𝑤
=
𝑆𝐹
𝑇𝑠
That is chirp rate 𝑅𝑏 which is equal to data rate is given as
𝑅𝑏 = 𝑅𝑠2𝑆𝐹
𝑐ℎ𝑖𝑟𝑝𝑠 /𝑠𝑒𝑐 (11)
Equation 11 suggests that symbol rate R_s varies inversely with spreading factor SF. Noise
resilience increases with enhanced SF. Thus by utilizing CSS with higher SF can enhance the
range of transmission. Robustness of communication in terms of Bit Error Rate (BER) can be
improved by using a suitable channel coding algorithm. Though LoRa protocol layers are kept
unpublished, the possibility of using hamming code (8,4) are revealed in many discussions.
Let us assume N set of symbols, chirp associated with any symbol 𝑛, 𝑛 ∈ [0, 𝑁 − 1] is unique.
All the N chirps are orthogonal to each other and can be retrieved without intersymbol
interference. Chirps for any symbol 𝑛 can be achieved by delaying 𝑓(𝑡) by
𝜏𝑛 =
𝑛
𝑏𝑤
𝑠𝑒𝑐𝑠 (12)
Figure 1 shows symbol 𝑛 modulated using up chirps delayed by 𝜏𝑛.
4. PERFORMANCE EVALUATION
Remote deployed sensor networks are constrained in energy, reliability, processing capability and
communication range. Majority of applications demand little or no direct human intervention.
When thousands of sensors are deployed, frequent replacement of batteries itself is laborious [14].
In order to save power, these devices are kept in sleep mode and awakened upon alerted or
scheduled. In this simulated version of CSS, preambles up chirps are transmitted by the remote
machine which intends a communication to the network. Simple ﬁlter circuits trigger interrupt
[15].

7
4.1. SIMULATION ENVIRONMENT
An equivalent baseband model has been created for up and down chirps for error-free simulations
of CSS. Modulated chirps were generated through linear phase variations keeping the amplitude
constant satisfying equation (8). Eight preamble chirps indicate the beginning of package
followed by two down chirps for synchronization. Symbols are generated from a binary
combination of SF [16]. Each symbol is a unique chirp orthogonal to each other. In order to
retrieve symbols at the receiver without inter symbol interference received signals are multiplied
by orthogonal down chirps. In figure 1 symbol n is modulated as chirps from [
−𝑇𝑠
2
,
𝑇𝑠
2
].
Chirps are spread as
𝑓𝑛(𝑡) =
𝑏𝑤
𝑇𝑠
(𝑡 − 𝜏) + 𝑏𝑤 for 𝑡 ∈ [−
𝑇𝑆
2
, −
𝑇𝑆
2
+
𝑛
𝑏𝑤
]
𝑓𝑛(𝑡) =
𝑏𝑤
𝑇𝑠
(𝑡 − 𝜏) for 𝑡 ∈ [−
𝑇𝑆
2
+
𝑛
𝑏𝑤
,
𝑇𝑆
2
] (13)
Figure 2. Coding and decoding process of CSS
4.2. SIMULATION RESULTS
Figure 3 shows chirps generated for 100 symbols which are transmitted with 8 preambles up
chirps and two synchronizing chirps. The generated chirps were transmitted through the AWGN
channel with Signal to Noise Ratio (SNR) 0db. Received signals after band pass filtering were
multiplied with orthogonal down chirps, to receive signal as shown in figure 4.
Fast Fourier Transform (FFT) performed on
Figure 3. 8 preamble, 2 sync and
100 symbols.
Figure 4. After multiplication with
orthogonal chirps at SNR 0db

8
received signals which were transmitted through AWGN channel with SNR 0db and -20db are
shown in figure 5 and figure 6 respectively.
On comparing FFT of spectrum received at SNR 0db and -20 dB, even though noise level is very
high at -20 dB, with SF = 10, clarity in peaks corresponding to symbols are observed. Figure 7
shows the simulated performance plot of CSS prepared for SF = 7 to 12, with Bandwidth (BW)
and sampling frequency are selected as 125kHz. With 8 preamble and 2 synchronization chirps, a
total of 27720 bits were decoded after being sent through AWGN channel for SNR from -40db to
0db. Bit Error Rates (BERs) were computed for 100 iterations.
Figure. 7: Plot of SNR vs BER for SF 7 to 12
Spectrograms of packet collisions, for a time span of 60 seconds at a time interval of 10
milliseconds are shown in figure 8. Evaluation is made with 6 channels and 500 devices
transmitting simultaneously for spreading factor 7 to 12. At a bandwidth of 125 kHz at ISM band
Figure 5. FFT performed after multiplying
with orthogonal chirps (transmitted at SNR
= 0dB and SF = 10)
Figure 6. FFT performed after multiplying
with orthogonal chirps (transmitted at SNR =
-20dB and SF =10)

9
868.7MHz to 869.2 MHz, it is observed that packet collisions are higher at SF = 11 and 12
compared with lower SFs.
Figure 8. Packet collisions with 500 sensors transmitting randomly for 60 seconds at 125kHz bandwidth.
Collisions occurred when data packets are transmitted randomly at 10 msec interval with steady
increasing packet rate per minute are shown in figure 9. Number of collisions and percentage
packet error rate vs number of bytes per minute are plotted.
Figure 9. Plot of number of collisions, packet error rate in percentage and number of bytes per minute with
1000 devices transmitting simultaneously with random spreading factor.
The plot of SNR vs. BER for SF 7 to 12 reveals the superior performance of CSS at a high noise
level. Acceptable level of BER is observed from -17db at SF = 7 to -30db at SF = 12. Extended
range can be achieved by enhancing spreading factor as shown in equation 11 but the bit rate is
compromised. Adversely when more devices communicate simultaneously at higher packet rate,
there are exponential increases in collisions and packet error. An optimum value can be observed
as 200 bytes per minute with 1000 device transmit simultaneously. Most of the sensor networks
in IoT application needs ultra low bit rate. A data rate of 200 bytes per minute is a substantially

10
high value for sensor networks. Even though Chirp Spread Spectrum can efficiently be deployed
for setting up ad hoc sensor networks for long-range concerns exists as the number of
deployments keeps on increasing, there shall be deterioration in performance due to packet
collisions at higher spreading factor. Alternate modulation schemes need to be considered for the
massive deployment of LPWAN.
5. CONCLUSIONS
We analyzed robustness and noise immunity of CSS as a modulation scheme for the deployment
of LPWAN. We investigated interference among carriers caused by simultaneous transmissions
for collisions. Observations prove better noise immunity of the modulation scheme and
suitability for low power wide area sensor networks. Collisions and packet error rate were plotted
for 1000 devices transmitting simultaneously at varying packet rate. Simulations proved an
exponential increase in collisions and packet error for simultaneous transmissions. Concerns are
justified on the deterioration of performance due to massive deployment. The inherent property of
chirp spread spectrum as energy efficient modulation scheme together with resilience to noise
makes it the best suited for sensor network IoT applications at the ultra-low bit rate. More
investigations need to be made to adopt methods to reduce mutual interference that may cause
due to massive deployment.
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[3] Guillaume Ferr´e, Eric Simon, (2018) “An introduction to Sigfox and LoRa PHY and MAC
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11
[10] Xiaowei Wang, Minrui Fei & Xin Li,(2008) “Performance of chirp spread spectrum in wireless
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[11] M. Winkler,(1962) ”Chirp signals for communications”, IEEE WESCON Convention Record, pp7.
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AUTHORS
Aiju Thomas received his Bachelor of Engineering and Masters of Technology in
Electronics and Communication Engineering with specialization in microwave
engineering. He is pursuing his research in the optimization of IoT protocols at M G
University, Kottayam, Kerala, India. With 10 years of industrial experience and 19
years as faculty in Electronics at Polytechnic institute, his field of interest include
industrial and embedded designing.
N V Eldhose received his Bachelor and Masters in Science and Ph.D. degree in Physics. As a research
guide for M G University, Kerala his research interests include ubiquitous computing, wireless sensor
networks, embedded systems, and machine-to-machine communication. He is currently a faculty in
Electronics at School of Technology and Applied Science and is guiding eight research projects currently.

SCALABILITY CONCERNS OF CHIRP SPREAD SPECTRUM FOR LPWAN APPLICATIONS

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SCALABILITY CONCERNS OF CHIRP SPREAD SPECTRUM FOR LPWAN APPLICATIONS